QJEEM22Ma3bf9: JEE Main 2022 Mathematics - Class 12 JEEM22Ma3bf9 Solution: The number of points where the function f ( x ) = {

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QJEEM22Ma3bf9: JEE Main 2022 Mathematics - Class 12 JEEM22Ma3bf9 Solution: The number of points where the function f ( x ) = {

The number of points where the function

$f (x) = {\begin{matrix} | 2 x^{2} - 3 x - 7 | & i f & x \leq - 1 \\ [4 x^{2} - 1] & i f & - 1 < x < 1 \\ | x + 1 | + | x - 2 | & i f & x \geq 1 \end{matrix}$

[t] denotes the greatest integer $\leq$ t, is discontinuous is _____________.

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Accepted Answer

\because f(-1)=2

and

f(1)=3

For

x \in(-1,1),\left(4 x^{2}-1\right) \in[-1,3)

hence

f(x)

will be discontinuous at

x=1

and also

whenever

4 x^{2}-1=0,1

or 2

\Rightarrow x = \pm \frac{1}{2}, \pm \frac{1}{\sqrt{2}} and \pm \frac{\sqrt{3}}{2}

So there are total 7 points of discontinuity.

QJEEM22Ma3bf9: JEE Main 2022 Mathematics - Class 12 JEEM22Ma3bf9 Solution: The number of points where the function f ( x ) = {

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